A fence that can be opened easily or jumped over will leave your construction site vulnerable to those who wish to take a look inside of your dumpsters. Install a chain link fence that is too hall to jump over and cannot be opened without taking off the lock. A heavy chain link fence will ensure that the openings of the fence cannot be kicked in, but that you will always be able to see what is happening on the site if you are on the outside looking in on the site. This will make it easier for reports of dumpster divers to get to you.
Although chaining and unchaining the dumpster will take a little bit more time during the opening of the day and the end of the day, this is the best way to stop divers. Putting a large chain on your trash can or even placing a lock on the lid if there is space will deter anyone from dumpster diving if they get onto your construction site. Be sure that the chain is double wrapped and cannot easily be slid off of the construction dumpster.
At the end of the day, before closing up the site, move the dumpster as close as you can get it to the building that is being worked on. Most people know that construction sites are dangerous and will tend to shy away from going near the actual construction. If you put the construction dumpster next to the building it provides camouflage and will make dumpster divers think twice before going near active construction.